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Jensen, Martin K
Published in
The B.E. Journal of Theoretical Economics

This paper considers ordered vector spaces with arbitrary closed cones and establishes a number of characterization results with applications to monotone comparative statics (Topkis (1978), Topkis (1998), Milgrom and Shannon (1994)). By appealing to the fundamental theorem of calculus for the Henstock-Kurzweil integral, we generalize existing resul...

Erlín Castillo, René

Se da una nueva demostración del teorema de Krein.

Sotnikov, A. I.
Published in
Siberian Mathematical Journal

The basic properties are studied of the ordered Banach algebra of strongly additive transition functions and some connections are dealt with the spaces of linear operators, vector measures, and measurable vector-valued functions. In particular, it is shown that every strongly additive transition function admits a (unique) decomposition into the sum...

Gutman, A. E. Sotnikov, A. I.
Published in
Siberian Mathematical Journal

The basic order properties, as well as some metric and algebraic properties, are studied of the set of finitely additive transition functions on an arbitrary measurable space, as endowed with the structure of an ordered normed algebra, and some connections are revealed with the classical spaces of linear operators, vector measures, and measurable v...

Aliprantis, C.D. Cornet, B. Tourky, R.
Published in
Positivity

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positiv...

Busch, Paul
Published in
Letters in Mathematical Physics

The disjointness of measures and their Hahn–Jordan decomposition are instances of the general notion of minimal decomposition in base normed spaces. The mixing distance, a specification of a novel concept of angle in real normed vector spaces, is applied to provide a geometric interpretation of disjointness as orthogonality.